Dissection of square to two identical polygons
Author : Gavin Theobald
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Square — 2×{n}
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2×{3}
Triangle
2×{4}
Square
2×{5}
Pentagon
2×{6}
Hexagon
2×{7}
Heptagon
2×{8}
Octagon
2×{9}
Enneagon
2×{10}
Decagon
2×{11}
Hendecagon
2×{12}
Dodecagon
2×{5/2}
Pentagram
2×{6/2}
Hexagram
2×{8/2}
Octagram
2×{8/3}
Octagram
2×{10/4}
Decagram
2×{12/2}
Dodecagram
2×{12/3}
Dodecagram
2×{R
_{√2}
}
Silver Rectangle
2×{R
_{ϕ}
}
Golden Rectangle
2×{R
_{2}
}
Domino
2×{G}
Greek Cross
2×{L}
Latin Cross
2×{G
_{c}
}
Curved Greek Cross
2×{L
_{c}
}
Curved Latin Cross
2×{M}
Maltese Cross
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
5
4
8
7
11
10
13
10
14
8
5/2
6/2
7/2
7/3
8/2
8/3
9/2
9/3
9/4
10/2
10/3
10/4
12/2
12/3
12/4
12/5
12
9
11
^{10}
10
16
15
^{14}
14
Square — 2 × Triangle (5 pieces)
Discovered by Ernest Irving Freese.
The dissection is translational.
Square — 2 × Square (4 pieces)
The dissection is translational and hingeable.
Square — 2 × Pentagon (8 pieces)
Square — 2 × Hexagon (7 pieces)
The dissection is translational.
Square — 2 × Heptagon (11 pieces)
Square — 2 × Octagon (10 pieces)
Square — 2 × Enneagon (13 pieces)
Square — 2 × Decagon (10 pieces)
Square — 2 × Hendecagon (14 pieces)
Square — 2 × Dodecagon (8 pieces)
Discovered by Ernest Irving Freese.
Square — 2 × Pentagram (12 pieces)
Square — 2 × Hexagram (9 pieces)
The dissection is translational.
Square — 2 × Octagram {8/2} (11 pieces)
Square — 2 × Octagram {8/2} (10 pieces with 3 turned over)
I discovered the original dissection, but Greg Frederickson worked out how to save a piece by turning over pieces.
Square — 2 × Octagram {8/3} (10 pieces)
Square — 2 × Decagram {10/4} (16 pieces)
Square — 2 × Dodecagram {12/2} (15 pieces)
Square — 2 × Dodecagram {12/2} (14 pieces with 1 turned over)
Square — 2 × Dodecagram {12/3} (14 pieces)
Square — 2 × Silver Rectangle (5 pieces)
The dissection is translational.
Square — 2 × Golden Rectangle (5 pieces)
The dissection is translational.
Square — 2 × Domino (2 pieces)
The dissection is translational.
Square — 2 × Greek Cross (4 pieces)
Discovered by Sam Loyd (1893).
The dissection is translational and hingeable.
Square — 2 × Latin Cross (7 pieces)
Square — 2 × Curved Greek Cross (13 pieces)
Square — 2 × Curved Latin Cross (16 pieces)
Square — 2 × Maltese Cross (12 pieces)
The dissection is translational and hingeable.
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Square — 2×{n}
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